Given the zero$-$mean sequence x$($n$)$x$($n$)$x$($n$)$ with autocorrelation

R$($m$)=$E$[$x$($n$)$x$($n$$m$)]=$a$$m$,$a$<1$R$($m$)=$ E$[$x$($n$)$x$($n$-$m$)]=$ a$^\{|$m$|\},\backslash$quad $|$a$|<1$R$($m$)=$E$[$x$($n$)$x$($n$$m$)]=$a$$m$,$a$<1$

$($i$)$ Find the coefficients of the following linear MMSE predictors of x$($n$)$x$($n$)$x$($n$)$:

x$^$i$($n$)=$j$=1$iaijx$($n$$j$),$i$=1,2,3\backslash$hat$\{$x$\}\_$i$($n$)=\backslash$sum$\_\{$j$=1\}^\{$i$\}$ a$\_\{$ij$\}$x$($n$-$j$),\backslash$quad i $=1,2,3$x$^$i$($n$)=$j$=1$i$$aij$$x$($n$$j$),$i$=1,2,3$

$($ii$)$ Find the corresponding MSEs.

$($iii$)$ If you see anything unusual in your results for different iii, comment on it and explain.